Getting second derivatives at every possible time point w.r.t. parameters

I have used ODEForwardSensitivityProblem to great effect to get derivatives of the equations in my system w.r.t the parameters at every possible time point.

Is there a way to get the Hessian at every possible time point?

https://diffeq.sciml.ai/stable/analysis/sensitivity/#Second-Order-Sensitivity-Analysis-via-second_order_sensitivities-(Experimental)

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Great to see the second-order sensitivities being implemented into Julia.

Still, one question remains for my case, not sure if it applies to @donkeysaddle’s case, too:
What if I don’t have a loss function with respect to which I want to calculate the Hessian, but I need the Hessian of the system’s ODE at points in time wrt some system parameters or the system’s initial state?
Then, I cannot use the system, or can I?
There’s a publication on how to derive higher-order sensitivities of ODEs/DAEs by Barrio from 2006 (https://doi.org/10.1137/030601892) which is what I would need

You can just use GitHub - JuliaDiff/TaylorSeries.jl: A julia package for Taylor polynomial expansions in one and several independent variables. for doing Taylor-mode automatic differentiation which is equivalent and more general.